2. Time
Superimposed
sinus waves
Amplitude
• Information can be transmitted by varying some
physical properties (e.g. current or frequency)
• Fourier Analysis (Fourier Series)
– Any function of time with period T can be represented as
– f = 1/T (fundamental freq.)
– The original signal (an,bn,c)
c can be reconstructed
László Böszörményi Computer Networks Physical Layer - 2
Theoretical Basis
s(t) = — c + Σ an sin(2πnft) + Σ bn cos(2πnft)
1
2 n=1 n=1
∞ ∞
an = — s(t) sin(2πnft) dt
0
T
2
T
3. László Böszörményi Computer Networks Physical Layer - 3
Non-periodic Signals
• A bit can be represented e.g. by amplitude of current
– E.g. the amplitude of “1” is +5mA that of “0” is -5mA
• Over long distance a periodic sinus signal (carrier)
can be modulated (e.g. ampl.) for representing bits
• Non-periodic signals (e.g. a bit pattern) can be
handled as repeating the entire pattern endlessly
– Example: Representation (and transmission) of character
“b“ as an 8-bit sequence “01100010“
0 1 1 1
0 0 0 0
s(t)
t
T
4. László Böszörményi Computer Networks Physical Layer - 4
Reconstruction
of Signals
• The Root-Mean-
Square (RMS =
√an
2 + bn
2) of the
amplitudes is
characteristic for the
energy of a given
frequency
• We need at least the
first 4 harmonics for
good signal
reconstruction
5. László Böszörményi Computer Networks Physical Layer - 5
Transmission Capacity
• Bandwidth (requirement) of a signal
– Difference of maximum and minimum Fourier frequency
• Bandwidth of a channel (link, transmission media)
– Frequency band within which transmitted signals are not
significantly distorted (up to link-specific cutoff frequency fc)
• Signaling speed (baud rate) (Jean-Maurice Baudot)
– Number of times per second that a medium physically
changes its value [baud]
• Data rate (bit rate)
– Number of bits transmitted per second [bits/s, bps]
– Bit rate b = (baud rate) * (number of bits per signal change)
6. László Böszörményi Computer Networks Physical Layer - 6
Maximum Data Rate on a Channel
Limited bandwidth of channel limits transmission rate
• Assume voice grade line (cut-off frequency: fc ≈ 3000 Hz)
• Bitrate is b [bit / sec] (Hz: After Heinrich Hertz)
b [bps] T = 8 / b [ms] f = b / 8 [Hz] nmax
300 26.67 37.5 80
600 13.33 75 40
1200 6.67 150 20
2400 3.33 300 10
4800 1.67 600 5
6000 1.33 750 4
9600 0.83 1200 2
19200 0.42 2400 1
38400 0.21 4800 0
• Time to transmit 8 bits:
T = 8 / b sec
• Frequency of 1. harmonic:
f = 1 / T = b / 8 Hz [1/sec]
• Frequency of n. harmonic:
f(n) = n * b / 8 Hz
• Number of highest
harmonic passed:
nmax* b / 8 Hz ≈ 3000Hz ⇒
nmax ≈ 3000 / (b/8) =
24.000 / b
7. László Böszörményi Computer Networks Physical Layer - 7
Harry Nyquist‘s Theorem (1924)
• If the highest frequency of a signal is H [Hz] (filtered at
H) then it can be reconstructed by >2H samples/sec
• If a noiseless channel can take V different values, the
maximum data rate bmax
NY of the channel is
bmax
NY = 2H ⋅ log2V [bps]
• Example
– H = 3000 Hz (voice grade line)
– V = 2 (binary signals, log2V =1)
– bmax
NY = 6000 bps = 6 Kbps
• Remark
– Noiseless channels do not exist
8. László Böszörményi Computer Networks Physical Layer - 8
Claude Shannon‘s Theorem (1948)
• If the bandwidth of a noisy channel (subject to, e.g.
thermal noise) is H [Hz] and the signal-to-noise ratio
(SNR) is S/N
– The maximum data rate bmax
SH of the channel
– bmax
SH = H ⋅ log2(1+S/N) [bps]
• If S << N ⇒ S/N ≈ 0 ⇒ bmax
SH = 0 (log2(1) = 0)
– This result is independent of signal levels / encoding!
• Example (cont‘d):
– H = 3.000 Hz
– S/N = 1.000 (i.e. SNR = 30 dB)
• SNR = 10•log10(S/N) [dB]) (log10(103) = 3)
– bmax
SH ≈ 3.000 * log2(1+1000) ≈ 30.000 bps (log2(1024)=10)
9. László Böszörményi Computer Networks Physical Layer - 9
Cables
• Twisted pair (UTP: Unshielded Twisted Pair)
– 2 insulated copper wires, twisted to avoid “antenna capabilities”
– The most usual connection for telephones
– Several kilometers without repeaters, several Mbit/sec
– UTP3: 16 MHz, UTP5: 100 MHz, UTP6-7: 250 – 600 MHz
• Coaxial Cable
– Up to 1 GHz
10. László Böszörményi Computer Networks Physical Layer - 10
Fiber Optics
a) Three examples of a light ray from inside a silica fiber impinging on
the air/silica boundary at different angles
b) Light trapped by total internal reflection
• Several rays with different angles: multimode fiber
• Speed goes from 10 Gbps up to 50 Tbps …
• Greatest problem: optical switching, optical ←→ electrical
• Communication may become faster than computation!
11. László Böszörményi Computer Networks Physical Layer - 11
Fiber Cables
a) Side view of a single fiber.
b) End view of a sheath with three fibers.
12. László Böszörményi Computer Networks Physical Layer - 12
Fiber Cables (2)
• A comparison of semiconductor laser and light
emission diodes (LEDs) as light sources
13. László Böszörményi Computer Networks Physical Layer - 13
Fiber Optic Networks
• A fiber optic ring with active repeaters
– Purely optical repeaters also available
14. László Böszörményi Computer Networks Physical Layer - 14
Wireless Transmission
• In vacuum, electromagnetic waves travel with
– ~3*108m/sec (~ 1 foot/nsec) (= speed of light), ca. 2/3 of this elsewhere
– λf = c (wavelength*frequency = constant)
– λf ≈ 300 (if λ in meters, f in MHz)
– Up to 8 bits at high frequencies (e.g. at 750MHz bandwidth: 6 Gb/s)
• Microwave Transmission (see also satellite)
– Above 100 MHz waves travel nearly straight – well focused (TV dish)
– With directed antennas excellent signal/noise can be reached
– Widely used for long distance telephone, mobile phone, TV
– Relatively inexpensive, microwave towers need few place
– Do not pass buildings well and depends on weather (rain)
• Infrared and Millimeter Waves
– For remote controls, do not pass walls
• Radio Transmission
15. László Böszörményi Computer Networks Physical Layer - 15
The Electromagnetic Spectrum
• The electromagnetic spectrum used for communication
– Low, medium, high, very, ultra, super, extremely, tremendously high f.
16. László Böszörményi Computer Networks Physical Layer - 16
Radio Transmission
a) In VLF, LF, MF bands, radio waves follow the curvature of the earth
(ca. 1000 km), power falls off sharply
b) In the HF and VHF band, they travel rather in straight lines and
bounce off the ionosphere (at 100-500 km)
– Easy to generate, can long distances, penetrate buildings
– Omnidirectional (can interfere with normal radio,e.g. police)
17. László Böszörményi Computer Networks Physical Layer - 17
Communication Satellites
• Microwave repeaters in the sky
– Broadcast is for free, good for apps, bad for security
• Geostationary Earth Orbit (GEO) Satellites
– Satellites at 35,800 km from earth remain “motionless”
– Spaced by 2 degrees, the max. number is 180 (=360/2)
– Slot/frequency allocation by ITU – highly political issue
– Big latency (270 ms)
• Medium-Earth Orbit (MEO) Satellites
– Move slowly (6 hours around the Earth), used for GPS
• Low-Earth Orbit (LEO) Satellites
– Move fast: elements of a chain replace each other
18. László Böszörményi Computer Networks Physical Layer - 18
Communication Satellites
• Communication satellites and some of their properties,
including altitude above the earth, round-trip delay time
and number of satellites needed for global coverage.
19. László Böszörményi Computer Networks Physical Layer - 19
Low-Earth Orbit Satellites
Iridium (77 LO satellites first, at 750 km)
a) The Iridium satellites form six necklaces around the earth
b) 1628 moving cells (253,440 channels) cover the earth
20. László Böszörményi Computer Networks Physical Layer - 20
Globalstar
a) Iridium: Relaying in space
b) Golbalstar: Relaying on the ground
– Complexity is managed in ground stations
21. László Böszörményi Computer Networks Physical Layer - 21
Public Switched Telephone System
• Structure of the Telephone System
• The Local Loop
– Modems
– ADSL
– Wireless
• Trunks and Multiplexing
• Switching
22. László Böszörményi Computer Networks Physical Layer - 22
Structure of the Telephone System
a) Fully-interconnected network (not practical!)
b) Centralized switch (scales wrong)
c) Two-level hierarchy ⇒ eventually 5 levels
23. László Böszörményi Computer Networks Physical Layer - 23
Structure of the Telephone Sys. (2)
1. Local loop
– Usually analog, twisted pair, distance 1-10 km
– Ca. 22.000 end offices in the USA
2. Trunks
– Digital fiber optics, connecting switching offices
3. Switching offices
24. László Böszörményi Computer Networks Physical Layer - 24
Internet over the telephone system
• The fixed telephone system
25. László Böszörményi Computer Networks Physical Layer - 25
Local Loop: Modems, ADSL and Wireless
• Direct current, digital signals in computer
• Alternating current, analog signals for transmission
• Conversion is done by the modems and codecs
26. László Böszörményi Computer Networks Physical Layer - 26
Modems
(a) A binary signal
(b) Amplitude modulation
(c) Frequency modulation
(d) Phase modulation
modulated
sine wave
carrier
modulated
sine wave
carrier
modulated
sine wave
carrier
27. László Böszörményi Computer Networks Physical Layer - 27
Modems (2)
(a) QPSK (Quadrature Phase Shift Keying): 2 bits/baud
(b) QAM-16 (Quadrature Amplitude Modulation): 4 bits/baud;
Can send 9,6 kbps over a (usual) 2400 baud line
(c) QAM-64: 6 bits/baud (14,4 kbs)
45°
135°
225° 315°
28. László Böszörményi Computer Networks Physical Layer - 28
Modems (3)
(a) (b)
(a) V.32 for 9, 6 kbps (4 data bits + 1 parity bit)
(b) V.32bis (QAM-128): 14,4 kbps (6+1, in fax modems)
• V.34bis: 33,6 Kbps – 35 Kbps is the limit by Shannon’s law
• V90: 56Kbs – limit by Nyquist’s law, using 7-bit data bytes
29. László Böszörményi Computer Networks Physical Layer - 29
Digital Subscriber Lines (1)
• The usual 4KHz (voice) filter is omitted (xDSL comm.)
• Bandwidth versus distance over category 3 UTP for DSL
• Dilemma of providers: distance vs. speed
30. László Böszörményi Computer Networks Physical Layer - 30
Digital Subscriber Lines (2)
• ADSL (Asymmetric DSL), discrete multitone modulation
– 1. Channel for POTS (Plain Old Telephone Service)
– 2-7. Channel: empty (separation) + control
– Data: asymmetric partitioning for up/downstream (32/217)
– Up/down speeds (Kbps): 768/8192, …1024/16384, 4096/30720
31. László Böszörményi Computer Networks Physical Layer - 31
Digital Subscriber Lines (3)
• A typical ADSL equipment configuration
32. László Böszörményi Computer Networks Physical Layer - 32
Internet over Cable (Television)
• Cable bandwidth is shared among the households
33. László Böszörményi Computer Networks Physical Layer - 33
Spectrum Allocation
• Frequency allocation in a typical cable TV system used for Internet access
• Analog modulation is used
– QAM-64 or QAM-256 downstream (≈30-40 Mbps), QPSK upstream
34. László Böszörményi Computer Networks Physical Layer - 34
Cable Modems
• Typical details of the upstream and downstream channels in US
• DOCSIS (Data Over Cable Service Interface Specification): standard
• At switch on
– Modem looks for system-packet and announces itself.
– In response, it gets its down/up channels from the head-end
– Ranging: modem determines its distance from head for proper timing with minislots
– For up-stream contention is possible: similar to slotted Aloha
